Method of calibrating a caliper AFM

ABSTRACT

A caliper atomic force microscope (AFM) comprises two AFM probes (each comprised of an oscillator and an attached tip) that operate on a sample in a coordinated manner. The coordinated operation of the AFM probes may be spatially or temporally coordinated. The result of the coordinated operation may be an image of the sample or a dimensional measurement of an unknown sample. The probes of the caliper AFM may be tilted, or the tips may be tilted at a non-orthogonal angle with respect to the probes, so as to enable the tips to access vertical sample surfaces or to enable the tips to touch each other. The tip shapes may include conical, boot-shaped, cylindrical, or spherical and materials from which the tips are fabricated may include silicon or carbon nanotubes. The oscillators may be beveled to allow the tips to operate in close proximity or in contact without interference of the oscillators. The disclosure of the present invention is discussed in terms of an atomic force (van der Waalls) interaction. Other interaction forces are contemplated, such as electrostatic force, magnetic force, and tunneling current. The caliper AFM may be calibrated with the help of a sample with known dimensions or by touching the probe tips. The tip-to-tip calibration enables absolute measurements without the need for a reference artifact, and it enables in-line calibration that may be performed during the measurement process.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of the following two U.S.Provisional Applications and the parent of this divisional application(namely, U.S. Provisional application Ser. No. 10/115,274, all of whichare hereby incorporated by reference:

COMMONLY OWNED AND PREVIOUSLY FILED U.S. PROVISIONAL PATENT APPLICATIONSSer. No. Title Filing Date 60/280,193 Caliper AFM for near- Mar. 30,2001 model-independent nanometrology 60/287,822 Multiple head caliperMay 1, 2001 atomic force microscope 10/115,274 Caliper Method, Systemand Apr. 1, 2002 now U.S. Pat. No. Apparatus 6,955,078 11/084,336Caliper, Method System and Mar. 18, 2005 now abandoned Apparatus

The benefit of 35 U.S.C. § 120 is claimed for all of the abovereferenced commonly owned applications. The contents of the applicationsreferenced in the table above are not necessarily identical to thecontents of this application.

All references cited hereafter are incorporated by reference to themaximum extent allowable by law. To the extent a reference may not befully incorporated herein, it is incorporated by reference forbackground purposes and indicative of the knowledge of one of ordinaryskill in the art.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to atomic force microscopes(AFMs) and in particular to a Caliper AFM for nanometer-scale lengthmeasurements.

2. Description of Related Art

Conventional atomic force microscope (AFM) probes have been developed toperform nanometer-scale measurements on test surfaces, but while thosesolved many problems, significant problems remained. For example,calibration of such probes is difficult. Great effort must be expendedto characterize probe shape in the presence of tip wear, estimate thetip-surface force profile in the presence of surface contamination andvariable material composition, and calibrate the scanning stages andother electro-optical sensors and actuators in the presence ofmanufacturing defects and environmental noise.

In other countries, the only similar caliper work that we are aware ofis at the Physikalische Technische Bundesantstalt (PTB), the counterpartof NIST in Germany. This work involves caliper type measurement on amuch larger scale. Two opposed scanning tunneling probes are being usedto measure the lengths of gauge blocks. One alternative way of obtainingCD measurements with substantial probe modeling is to section the waferand obtain a cross-section SEM image. However, even on thinned sectionsthe edge resolution of SEMs is limited by the beam-sample interaction. Asecond and related approach is to manufacture thinned wafer sectionsthat can be measured in a transmission electron microscope. The edgeresolution of this approach is extremely good. However, the scalecalibration of TEM relies on comparison of the measured images withcalibrated artifacts, such as atomic lattice spacings, under nearlyidentical imaging conditions and is difficult to carry out with highprecision. Furthermore, both of these techniques are destructive andinvolve off-line measurements in vacuum.

BRIEF SUMMARY OF THE INVENTION

In accordance with an embodiment of the invention, a caliper atomicforce microscope (AFM) includes a first AFM probe having a first tip,and a second AFM probe having a second tip. The caliper AFM isconfigured such that the first tip and the second tip can measure a testsample in a coordinated manner.

Optionally, the caliper AFM may be configured so that the first tip canmove and the second tip can move. The moves may be coordinated. Themoves may be relative to a test sample. The coordination may betouch-probing. The move of the first tip may occur relative to the testsample. The first tip may move, the second tip may move, and the testsample may be stationary. The first tip may move, the second tip may bestationary, and the test sample may move. The first tip may bestationary, the second tip may be stationary, and the test sample maymove. The first tip and the second tip may be stationary relative toeach other, and the test sample may move. The first tip and the secondtip may be stationary relative to each other, and the test sample may bestationary. The first tip may move, the second tip may move, and thetest sample may move. The first tip may move in only one dimension. Thefirst AFM probe may be configured to tilt on a first axis to enable thefirst tip to move close to the second tip. The shape of the first tipmay be boot-shaped, cylindrical shaped, carbon nanotube, or spherical,and the shape of the second tip may be boot-shaped, cylindrical shaped,carbon nanotube, or spherical. The first AFM probe may not be configuredto tilt, and the first tip may be tilted to enable the first tip to moveclose to the second tip. The first AFM probe may include a firstoscillator on which the first tip is mounted and the first oscillatormay be beveled to allow the first tip to move close to the second tipwithout contacting the second AFM probe. The first AFM probe may includea first multiresonant oscillator on which the first tip is mounted; andthe second AFM probe may include a second multiresonant oscillator onwhich the second tip is mounted. A caliper AFM system, may comprise aplurality of caliper AFMs. The plurality of caliper AFMs comprising acaliper AFM system may be configured to measure the test sample in acoordinated manner.

According to another embodiment of the invention, a method of testsample measurement using a caliper that has a first tip of a first AFMprobe and a second tip of a second AFM probe includes positioning thefirst tip on a first surface of the test sample, positioning the secondtip on a second surface of the test sample, creating a first data set bymeasuring the test sample with the first tip, and creating a second dataset by measuring the test sample with the second tip and the first tipand the second tip are operably coordinated.

Optionally, the creating of a first data set may include creating afirst data set by measuring the test sample with the first tip inreference to the second tip and the creating a second data set mayinclude creating a second data set by measuring the test sample with thesecond tip in reference to the first tip. The first data set may includea first relatively referenced data set and the second data set mayinclude a second relatively referenced data set. The first relativelyreferenced data set and the second relatively referenced data set may bethe same. The creating of a first data set may include creating a firstdata set by measuring the test sample with the first tip in reference toa global coordinate system, and the creating of a second data set mayinclude creating a second data set by measuring the test sample with thesecond tip in reference to the first tip. The first data set may includea first globally referenced data set and the second data set may includea second relatively referenced data set. The creating of a first dataset may include creating a first data set by measuring the test samplewith the first tip in reference to a global coordinate system and thecreating of a second data set may include creating a second data set bymeasuring the test sample with the second tip in reference to the globalcoordinate system. The first data set may include a first globallyreferenced data set and the second data set may include a secondglobally referenced data set. The method of test sample measurement mayinclude a plurality of measurements. The plurality of measurements maybe at least part of a transverse scan. The plurality of measurements maybe at least part of a longitudinal scan. The tips may not touch the testsample between measurings nor during measurings. The tips may touch thetest sample between measurings and during measurings. The tips may nottouch the test sample between measurings; and the tips may touch thetest sample during measurings. Measuring the test sample with the firsttip may occur at approximately the same time as the measuring of thetest sample with the second tip. Measuring the test sample with thefirst tip may not occur at approximately the same time as the measuringthe test sample with the second tip. The first tip and the second tipmay be positioned so that at least one of their coordinates isapproximately equal.

According to another embodiment of the invention, a method ofcalibrating a caliper that has a first tip of a first AFM probe and asecond tip of a second AFM probe includes taking a measurement of anartifact having a known dimension; and adjusting the caliper based onthe difference between the measurement and the known dimension.

Optionally, the taking of the measurement may include taking ameasurement of an artifact having a known dimension while the tips arein contact with the artifact. The taking of the measurement may includetaking a measurement of an artifact having a known dimension, using theextreme lateral points of the tips, while the tips are in contact withthe artifact. The taking of the measurement may include taking ameasurement of an artifact having a known dimension, using the extremevertical points of the tips, while the tips are in contact with theartifact. The taking of the measurement may include taking a measurementof an artifact having a known dimension, while the tips are not incontact with the artifact. The taking the measurement may include takinga measurement of an artifact having a known dimension, using the extremelateral points of the tips, while the tips are not in contact with theartifact. The taking of the measurement may include taking a measurementof an artifact having a known dimension, using the extreme verticalpoints of the tips, while the tips are not in contact with the artifact.The first tip may have a first apex, the second tip may have a secondapex, and the taking of the measurement may include characterizing theapexes using an artifact having a known dimension.

According to another embodiment of the invention, a method ofcalibrating a caliper that has a first tip of a first AFM probe and asecond tip of a second AFM probe includes positioning the tips such thatthey are at a known tip-to-tip distance for which they have an knowninteraction, measuring a measured interaction of the tips; and adjustingthe caliper based on the difference between known interaction andmeasured interaction.

Optionally, the positioning may include positioning the tips such thattheir extreme lateral points are at a known tip-to-tip distance forwhich they have a known interaction; and the measuring may includemeasuring a measured interaction of the extreme lateral points of thetips. The measuring may include characterizing the each apex with theother apex.

According to another embodiment of the invention, a method ofcalibrating a caliper AFM that has a first tip of a first AFM probe anda second tip of a second AFM probe, wherein the first AFM probe canmove, and wherein the second AFM probe can move, such that the first tipand the second tip coordinate in a caliper manner, includes at least onecalibrating the tips, and at least one measuring the test sample withthe caliper AFM. The calibrating of a caliper AFM may include in-linecalibration. The calibrating of a caliper AFM may include controllingthe operation of the method by a logic circuit. The controlling of theoperation of the method by a logic circuit may include controlling theoperation of the method by a logic circuit responsively to the resultsof past operations of the method.

According to another embodiment of the invention, a method of traceablymeasuring a test sample using a caliper that has a first tip of a firstAFM probe and a second tip of a second AFM probe, includes traceablycalibrating the caliper AFM, traceably positioning the first tip on afirst surface of a test sample, traceably positioning the second tip ona second surface of the test sample, creating a first traceable data setby measuring the test sample with the first tip, and creating a secondtraceable data set by measuring the test sample with the second tip.

Optionally, traceably calibrating the caliper AFM may include taking ameasurement of an artifact having a traceable known dimension, andadjusting the caliper based on the difference between the measurementand the known dimension. Traceably calibrating the caliper AFM mayinclude positioning the tips such that they are at a known tip-to-tipdistance for which they have a known interaction, measuring a measuredinteraction of the tips, and adjusting the caliper based on thedifference between known interaction and measured interaction.

In accordance with yet another embodiment of the invention, a measuringsystem includes a first AFM probe having a first tip and a firstreflective surface. The system also includes a control circuit adaptedto cause the first AFM probe to move the first tip relative to a testsample and a collimated laser source configured to produce a collimatedlaser, wherein the collimated laser is directed so that the firstreflective surface falls within the collimated laser, whereby the firstreflective surface produces a first reflection. The system would furtherinclude a first mirror, configured to receive the first reflection,whereby the first mirror produces a first further reflection, a positionsensitive detector (PSD) configured to receive the first furtherreflection, and a measurement circuit adapted to ascertain, based on thePSD's output, a first point on the test sample.

The system might also include a second AFM probe with a tip andreflective surface and a second mirror, wherein the control circuit isadapted to cause the second AFM probe to move the second tip relative tothe test sample, the collimated laser is directed so that the secondreflective surface falls within the collimated laser, whereby the secondreflective surface produces a second reflection, wherein the secondmirror is configured to receive the second reflection, whereby thesecond mirror produces a second further reflection, wherein the PSD isconfigured to receive the second further reflection, and wherein themeasurement circuit is adapted to ascertain, based on the PSD's output,a second point on the test sample. The first reflective surface mighthave a first fiducial and the second reflective surface might have asecond fiducial. The first AFM probe might include a first cantilever,to which the first tip is attached, and the first reflective surfacemight include all of at least one face of the first cantilever, whereinthe first AFM probe includes a second cantilever, to which the secondtip is attached, and the second reflective surface includes all of atleast one face of the second cantilever. The PSD's output includes an ACsignal and a DC signal, wherein the measurement circuit is configured tosimultaneously process the AC signal and the DC signal in ascertainingthe first point on the test sample and the second point on the testsample. The first AFM probe might have a first mounting chip with abevel and a first cantilever with a first end and a second end, whereinthe first end is attached to the first mounting chip and the first tipis attached to the second end, wherein the first reflective surface islocated on the bevel. The first AFM probe might have a first mountingchip and a first cantilever having a first end and a second end, whereinthe first end is attached to the first mounting chip, and wherein thefirst tip is attached to the second end, wherein the first reflectivesurface comprises a fiducial located on the first mounting chip.

In accordance with a still further embodiment of the present invention,a method of measuring a test sample includes ascertaining a firstplurality of points on a first sidewall of the test sample with a firstAFM probe, wherein the first plurality of points is included in a firstline roughness (LR).

The first LR of the method might include a transverse LR or alongitudinal LR. If the LR is measured along an edge of the firstsidewall, it would be a line edge roughness (LER). Sidewall roughness(SWR) could be measured by combining LR measurements. The method mightinclude ascertaining a second plurality of points on a second sidewallof the test sample with a second AFM probe, wherein the second pluralityof points is included in a second LR, the first AFM probe and the secondAFM probe coordinate in a caliper manner, the second LR is positionallyapproximately opposite the first LR, and a linewidth roughness (LWR),comprising the first LR and the second LR, is measured.Three-dimensional linewidth roughness (3DLWR) could be made by combiningLWR measurements.

In accordance with another embodiment of the invention, a method ofmeasuring a test sample includes measuring a line roughness (LR) using aprobe and determining spatial frequency data based on the LR usingFourier Transform (FT).

The LR might comprise fractals or wavelets. The probe might be an AFM,SEM, or reflectometry probe.

In accordance with another embodiment of the invention, a MEMS caliperapparatus includes a first AFM oscillator having a first tip, a secondAFM oscillator having a second tip, wherein the first AFM oscillator andthe second AFM oscillator are configured so as to be able to move withrespect to each other in three dimensions, a control circuit thatcontrols the movement of the first AFM oscillator and the movement ofthe second AFM oscillator, and a sensing circuit that measures a testsample based on the first AFM oscillator's output and the second AFMoscillator's output.

The control circuit and the sensing circuit may be integrated. Theapparatus may include a substrate, an arm, from which the first AFMoscillator and the second AFM oscillator extend, a flex link, whereinthe arm is attached to the substrate by the flex link, which allowsthree degrees of freedom, and wherein the substrate, the flex link, thearm, the first AFM oscillator, the second AFM oscillator, the first tip,and the second tip are included in a single measuring structure. Thefirst and second tips might each include a vertical tip having a firstend and a horizontal tip attached to the first end, opposite which thehorizontal tip has an apex, wherein the apexes can touch. The first tipmay have a first apex, wherein the first tip is tilted such that thepart of the first tip closest to the second tip is the first apex, thesecond tip has a second apex, the second tip is tilted such that thepart of the second tip closest to the first tip is the second apex, andthe apexes can touch.

In accordance with another embodiment of the invention, a method ofdetecting extreme lateral tip points includes bringing a first tip and asecond tip into lateral proximity, wherein the first tip has a firstextreme lateral point and is included in a first AFM probe, and whereinthe second tip has a second extreme lateral point and is included in asecond AFM probe; scanning in two dimensions of a plane approximatelyorthogonal to an imaginary line between the first tip and the secondtip; and wherein maximum tip distance indicates that the first extremelateral point is touching the second extreme lateral point.

BRIEF DESCRIPTION OF THE DRAWINGS

The following drawings form part of the present specification and areincluded to further demonstrate certain aspects of the presentinvention. The figures are not necessarily drawn to scale. The inventionmay be better understood by reference to one or more of these drawingsin combination with the detailed description of specific embodimentspresented herein.

FIG. 1 shows a boot-shaped probe making a conventional linewidthmeasurement, in accordance with prior art.

FIG. 2-A shows a calibration of a caliper AFM, in accordance with anembodiment of the present invention. [FIG. 2-B shows a calibration of aprior art AFM]

FIGS. 3-A and 3-B show scan paths of caliper AFM tips, in accordancewith an embodiment of the present invention.

FIG. 4 shows a caliper AFM system, in accordance with an embodiment ofthe present invention.

FIG. 5 shows two probes coordinating as a caliper, in accordance with anembodiment of the present invention.

FIG. 6 shows a caliper AFM configuration with scanned probes and astationary test sample, in accordance with an embodiment of the presentinvention.

FIG. 7 shows a caliper AFM configuration with stationary probes and ascanned test sample, in accordance with an embodiment of the presentinvention.

FIG. 8 shows a tilted probe in accordance with an embodiment of thepresent invention.

FIG. 9 shows two tilting probes coordinating as a caliper, in accordancewith an embodiment of the present invention.

FIG. 10 shows a mechanism for tilting AFM probe, in accordance with anembodiment of the present invention.

FIG. 11—Measurement using a caliper AFM

FIG. 12—An illustration showing paths of transverse and longitudinalscans

FIG. 13—Line roughness (LR) measurements along a transverse and alongitudinal path on the surface of a feature

FIG. 14—Illustration of a Y raster scan

FIG. 15 shows a logic of utilizing a reflective fiducial mark forsensing the AC and DC position of a caliper AFM probe, in accordancewith an embodiment of the present invention.

FIG. 16 shows use of a reflective fiducial mark for navigating thecaliper AFM probe to a target location on a wafer, in accordance with anembodiment of the present invention.

FIG. 17 Non contact mode measurement

FIG. 18—Extreme lateral and vertical points of left probe tip(Illustrated in two dimensions)

FIG. 19—Illustration showing how sharper tips can shrink the requiredarcs to arbitrarily small sizes in the case of a Caliper AFM

FIGS. 20-A and 20-B show a reference linewidth measurement and alinewidth measurement using a caliper AFM, in accordance with anembodiment of the present invention.

FIG. 21—Calibration of a caliper AFM using an artifact having knowndimensions

FIG. 22—Calibration of a caliper AFM using the lateral extreme points ofthe tips

FIG. 23—Calibration of a caliper AFM using the vertical extreme verticalpoints of the tips

FIG. 24—Non-contact mode calibration of a caliper AFM using an artifacthaving known dimensions

FIG. 25—Example of calibration with extreme lateral points at a knowntip-to-tip distance

FIG. 26—Contact mode calibration of a caliper AFM

FIG. 27—Example illustrating characterization of left tip by right tip.

FIG. 28—Example illustrating characterization of right tip by left tip.

FIG. 29—Line roughness (LR) measurement along an arbitrary path on thesurface of a feature

FIG. 30—Sidewall roughness (SWR) measurement made in a region ofinterest on the feature surface

FIG. 31—Line roughness measurements made to determine linewidthroughness

FIG. 32—Line edge roughness (LER) measurement made along a path thattraverses the edge of a feature

FIG. 33—Three-dimensional linewidth roughness (3DLWR) measurement

FIG. 34 shows a spatial spectrum of probe data, in accordance with anembodiment of the present invention.

FIGS. 35-A and 35-B show the position of the test sample as it isscanned by a caliper AFM with stationary probes and scanned test sample,in accordance with an embodiment of the present invention.

FIG. 36 shows the scanned path of the caliper AFM with stationary probesand scanned test sample, in accordance with an embodiment of the presentinvention.

FIGS. 37-A and 37-B show two possible layouts for multiple-head caliperAFM systems, in accordance with an embodiment of the present invention.

FIG. 38 shows a MEMS caliper embodiment of the present invention.

FIG. 39 shows a top view of MEMS cantilevers with probe tip structuresattached

FIG. 40 shows a top view of MEMS slanted cantilevers with probe tipstructures attached

FIG. 41 shows an end view of MEMS probe tip structures with carbonnanotubes attached

FIG. 42 shows an end view of MEMS probe tip structures with tips mountednear inner sides of cantilevers

FIG. 43 shows an end view of MEMS probe tip structures slanted inward tofacilitate imaging of a feature

FIG. 44 shows an end view of MEMS probe tip structures with invertedumbrella shaped probe tips

FIG. 45 shows an end view of MEMS probe tip structures with pointedshapes pointing inward toward the feature

FIG. 46 shows a top view of MEMS probe tip structures with pointedshapes pointing inward toward the feature

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Throughout this description, primed reference characters correspond tounprimed reference characters. For example, reference character 1′ wouldcorrespond to the reference character 1.

The Problem Solved by the Present Invention

The main disadvantage of scanning-probe measurement tools is theirdependence on a priori knowledge of the probe's shape and itsinteraction with the test sample to reconstruct the dimensions of thetest sample from raw measurement data. In the case of a conventionalatomic force microscope (AFM), great effort must be expended tocharacterize probe tip shape in the presence of tip wear, estimate thetip-surface force profile in the presence of surface contamination andvariable material composition, and calibrate the scanning stages andother electro-optical sensors and actuators in the presence ofmanufacturing defects and environmental noise.

Model dependence refers to reliance on such a priori information aboutoperation of a measurement tool that must be removed from raw data toextract a quantity of interest. Calibration is the process ofdetermining the required a priori information by measuring some knownquantity and adjusting the output of the measurement tool so that itprovides the correct reading. The larger, more complex, and morevariable its model dependence, the more difficult it is to calibrate ameasurement tool.

There are two approaches for dealing with model dependence. One approachis to accept the conventional architecture of the measurement tool forwhat it is and attempt to determine all of the a priori informationrequired to calibrate it. The alternative approach adopted in thepresent invention rejects conventional AFM design in favor of anentirely new dual-scanning-probe caliper architecture that is virtuallymodel-independent. Taken together, removal of the three major sources ofuncertainty in scanning probe tools provides an exciting opportunity todemonstrate a revolutionary new breed of AFM metrology tool that pavesthe way for scanning probe measurements that are both precise (i.e.,highly repeatable) and accurate (i.e., traceable to referenceartifacts).

The semiconductor industry represents an important example illustratingthe utility of the present invention. Critical dimension metrology offeatures involved in semiconductor manufacturing relies on extensivemodeling of measurement tool-induced uncertainties, and on therepeatability of measurements to keep the manufacturing process undercontrol. This conventional approach is rapidly nearing the end of itsusefulness as feature sizes shrink to the level where measurement tooluncertainties dominate the measurement process. Therefore, a newapproach for length metrology is required.

The Problem of Tip Shape Uncertainty

Recording the motion of the tip of a scanning probe measurement toolwith respect to a sample surface provides an image of the surface thatis convolved with the shape of the probe tip. The shape of the tip mustbe deconvolved from the scanned image to generate the true topography ofthe sample. For pitch and height measurements this may not be a criticallimitation, since two respective points on the feature surface can bemeasured by the same point on the tip. Pitch and height measurements cantherefore be recovered with acceptable uncertainty even in the presenceof poor knowledge about the tip shape. For feature width measurements,however, uncertainty in the tip shape translates directly intomeasurement uncertainty whenever different points on a single probe tipare used to make measurements. Conventional single-tip scanning probetools are inherently limited by the need to perform frequent, extensivecharacterization of tip shape.

Referring to FIG. 1, The problem of tip shape uncertainty is illustratedby comparing a linewidth measurement made with a conventional AFM havinga single boot-shaped tip 100 and a linewidth measurement with adual-probe caliper AFM. The linewidth measurement w_(boot) obtained witha single boot-shaped tip is:w _(boot)=(y−pw _(R) −sf _(R))−(x+pw _(L) +sf _(L))w _(boot)=(y−x)−(pw _(R) +pw _(L))−(sf _(R) +sf _(L))w _(boot)=(y−x)−pw−sf  (1)w _(boot)=(y−x)−pw  (2)where x and y are the respective left and right stage positions asrecorded by the sensing system of the scanning stage, pw_(R) and pw_(L)are the respective right and left probe widths, pw is the total probewidth, sf_(R) and sf_(L) are the respective right and left tip-surfacedistances, and sf is the total combined tip-surface distance of themeasurement. As can be seen from Equation 1, the linewidth w_(boot)depends on the probe width pw and the tip-surface distance sf. Assumingthat the mode of scanning is contact, the linewidth w_(boot) is still afunction of the probe width pw, as can be seen from Equation 2.

Referring to FIG. 2, The present invention solves this problem by usingdual scanning probes, 200 and 201, that operate in coordinated fashionas a caliper, instead of reliance on a single probe tip. This allowsdifferent regions on the surface of a convex or concave feature to bemeasured by points on the surfaces of two different probe tips. Theequivalent linewidth measurement w_(caliper) obtained by the caliper AFMwith two tips would be:w _(caliper)=[(y−pw _(R) −sf _(R))−(x+pw _(L) +sf _(L))]−[(y _(R) −pw_(R) −sf _(R)′)−(x _(R) +pw _(L) +sf _(L)′)]w _(caliper)=[(y−x)−(pw _(R) +pw _(L))−(sf _(R) +sf _(L))]−[(y _(R) −x_(R))−(pw _(R) +pw _(L))−(sf _(R) ′+sf _(L)′)]w _(caliper)=[(y−x)−pw−sf]−[(y _(R) −x _(R))−pw−sf′]w _(caliper)=(y−x)−(y _(R) −x _(R))−(sf−sf′)−pw+pww _(caliper)=(y−x)−(y _(R) −x _(R))−(sf−sf′)  (3)w _(caliper)=(y−x)−(y _(R) −x _(R))  (4)w _(caliper)=Δ−Δ_(R)  (5)where x and y are the respective left and right stage positions asrecorded by the sensing system of the scanning stage, and x_(R) andy_(R) are the respective reference stage positions as recorded by thesensing system of the scanning stage at the moment when the two tips aretouching each other to establish a known reference. In thisillustration, the known reference is a zero reference. The effectiveprobe width pw and tip-surface distance sf are defined the same way asfor the single probe measurement.

The left side of a convex feature can be measured by a left caliper tipand the right side of a convex feature can be measured by a rightcaliper tip. In the case of a concave feature, the situation is reversedwith the left side of the feature being measured by a right caliper tipand the right side of the feature being measured by a left caliper tip.A zero reference point can be established by bringing the left and rightcaliper tips together into a known reference configuration, for example,with the tips touching at their respective lateral extreme points. Thiszero referencing procedure provides the required calibration formeasurements of extension, such as line width and hole diameter.Alternatively, a reference artifact with a finite, known dimension canbe used to calibrate the measurement tool. Use of dual scanning probesthat operate together as a caliper virtually eliminates model-dependentuncertainties associated with probe tip shape for nanometer-scalemeasurements of extension, such as line width and hole diameter.

The Problem of Tip-to-Surface Interaction Uncertainty

Another major source of modeling uncertainty for a conventional scanningprobe tool is the tip-surface interaction. Tapping mode and non-contactmode of operation are the two methods most commonly used withconventional, single-probe AFMs. Tapping mode is the more stable of thetwo and is nearly independent of surface contamination effects. However,it relies on nonconservative energy dissipation of the tip in the atomicforce region of the surface to maintain the tip-surface gap constant.This mode of sensing requires an amplitude of oscillation of the probeof 10s of nanometers and hence a comparable uncertainty in its position.Non-contact mode depends on the long-range conservative surface forcesthat can strongly depend on surface contamination and can vary with thematerial composition of the sample. This dependence makes thenon-contact mode of operation also prone to variations and thereforegreater uncertainties. Therefore, there is a modeling relateduncertainty associated with both the short range, nonconservative forces(e.g., dissipation upon impact, surface contamination) and the longrange conservative forces (e.g., van der Waals profile). Contact moderelies on short-range (sub-nanometer) attractive surface forces andrequires no modeling of the tip-surface attractive interaction. However,scanning in contact mode can rapidly degrade both the tip and thesample.

Referring to FIGS. 3-A and 3-B, the present invention solves thisproblem by combined use of two sensing modes; non-contact mode scanningfor local navigation of the probes with respect to the samplealternating with independent touch-probing of the two scanning probetips with respect to the sample to obtain the required dimensionalmeasurement. Taking measurements during touch-probing, while the tip ismomentarily in contact with the sample surface, removes model-dependentuncertainties associated with tip-surface interaction from themeasurement data.

In general the tip-to-tip distance sf′ during a non-contact typeinteraction is different from the tip-surface distance sf. Nevertheless,the two distances cancel each other to minimize the effect of thetip-surface distance on the linewidth measurement (Equation 6), and, inthe preferred way, it is null for a touch-probe contact mode ofoperation (Equation 7). As can be seen from Equation 3, the probe widthpw does not enter into the computation of the linewidth w_(caliper), andthe effect of the tip-surface distance is minimized even for non-contactmode of operation. For touch-probe contact mode of operation, thelinewidth w_(caliper) is presented by Equation 4.(sf−sf′)<sf for non-contact mode of operation  (6)(sf−sf′)=0 for touch-probe contact mode of operation  (7)The Problem of Mechanical Loop Uncertainty

Another source of modeling uncertainties in scanning probe tools isassociated with mechanical loops in the system. The tip-sample loop viathe structure is an illustration of one such mechanical loop, where themechanical chain extends from the tip to the sample through theoscillator, the base of the oscillator, the clamping fixtures, thescanning stage, and the tool frame. Each of the mechanical structures inthe chain of the loop is subject to vibration, thermal expansion, andstress, as sources of uncertainty. Uncertainties due to mechanical loopscan be reduced by proper design, selection of temperature-stablematerials, and use of components with similar mechanical properties, butnevertheless impose severe limitations the achievable measurementprecision and accuracy when nanometer-scale feature dimensions areinvolved.

Referring to FIG. 4, the present invention solves this problem ofreducing measurement uncertainty introduced by mechanical loops by usinga sensing system in conjunction with use of dual scanning probes thatmakes a measurement involving the shortest possible mechanical loop fromthe right caliper tip to the left caliper tip. One way to accomplishthis is to measure the left-scan-stage-to-right-scan stage relativedistance directly. Each scanning stage can be calibrated accurately withexisting methods that are traceable (i.e., relatable to an absolutelength standard, such as a particular wavelength of light). The stageposition can be measured precisely (i.e., with high repeatability) withthe help of interferometric sensors or capacitive sensors that have beencalibrated with an interferometer. Two such calibrated scanning stageswill determine the relative stage-to-stage distance, 400, and thereforethe relative tip-to-tip distance. The relative tip-to-tip distanceprovides the measurement of extension, such as line width and holediameter. Alternatively, the relative probe-to-probe distance, andtherefore the relative tip-to-tip distance, can be directly measured byusing fiducial dots, 401 and 402, on the surfaces of the probes asreflective markers and a single continuous position sensitive detector,403, configured electronically to measure (through reflected lightbeams) the fiducials' positions and their relative distance. Therelative fiducial-to-fiducial distance and its projection on theaperture of the continuous position sensitive detector provides a scaledmeasurement of extension, such as line width and hole diameter. Thisprocedure is equivalent to directly measuring the respective differenceterms, (y−x), and (y_(R)−x_(R)) in Equation 4 rather than measuring xand y separately, taking the difference to get (y−x), measuring x_(R)and y_(R) separately, and taking the difference to get (y_(R)−x_(R)).The preferred procedure results in an overall reduction of measurementuncertainty because it enables four typically large errors associatedwith conventional stage-based measurements x, y, x_(R) and y_(R) to bereplaced with two relatively small errors associated with directmeasurement of the difference terms, (y−x), and (y_(R)−x_(R)).

Description of the Caliper AFM

In the basic embodiment of the present invention the Caliper AFM,illustrated in FIG. 5, comprises two atomic force microscope (AFM)probes that operate on a test sample in a coordinated manner. The resultof operating on a test sample can, for example, be to generate an imageof the test sample, to make a dimensional measurement of an unknown testsample, or to calibrate the caliper AFM based on measurement of a samplewith known dimensions.

The functioning of a single AFM probe is well known to those skilled inthe art. Coordination means that the probes are capable of workingtogether in a common operation, for example, to produce an image or ameasurement of the test sample. An example of coordination is theimaging of a resist line on a semiconductor circuit where each probeimages one side of the resist line and where the combination of the twoimages will produce the image of the entire resist line. Another exampleis the measurement of a polysilicon line on a semiconductor circuitwhere each probe measures the distance between a common reference and arespective side of a polysilicon line, where the combination of the twodistances will produce the linewidth of the polysilicon line. Thedetails of imaging a resist line and measurement of a polysilicon line,are known to those skilled in the art. Other examples of coordinatingthe operation of the probes of a caliper AFM include coordination forthe purpose of measuring a line edge roughness spectrum or a line widthroughness spectrum, coordination for the purpose of executing maneuversnecessary for transverse or longitudinal scanning, coordination for thepurpose of achieving clearance between the probe structures andcoordination for the purpose of achieving clearance between both probesand the sample.

Parallel operation on an array of AFMs, each of them operatingindependently (i.e., not working together) and not towards a commonoperation, is not an example of coordination of AFM probes as describedin the disclosed invention. The operation of micro-sized or nano-sizedtweezers that work together towards a common operation of grasping anobject is also not an example of coordination of AFM probes, asdescribed in the disclosed invention, because the tweezers' probes donot have AFM capabilities and cannot produce an image nor a measurement.

Another characteristic of the basic embodiment of the Caliper AFM isthat the probes are capable of working together in a common operation inmore than one manner. For example, the operation of each probe can bespatially or temporally coordinated. In a spatially coordinatedoperation the probes can operate on the same test sample feature or theycan operate on different sample features somewhat removed from eachother but still within the range of motion of both the probes. In aspatially coordinated operation on the same test sample feature theprobes can be aligned in any two of the tool-fixed XYZ coordinates orthey can be aligned in any one of the XYZ coordinates, or not be alignedat all. In temporally coordinated operation, the probes can operatesimultaneously, with some time lag, or one after another. In onerepresentative example, two spatially and temporally coordinated probescan image a polysilicon line on a semiconductor circuit in such a mannerthat that the probes are aligned in the Y raster direction and theirheight is kept the same in the Z direction while the probessimultaneously scan in the X direction and obtain an image in the XZplane. Several alternative caliper AFM embodiments that take advantageof different spatial and temporal coordination are described later inthis disclosure.

In another example of a common operation in more than one manner, theprobes and the sample stage can be arranged so that, during anoperation, the probes and the sample stage are either fixed, stationary(e.g., temporarily fixed), or moving (e.g., scanning), in anycombination with respect to each other and in respect to any degree offreedom of motion. In one example, illustrated in FIG. 6, the two probesare moving over a fixed sample stage, and in another example,illustrated in FIG. 7, the stationary probes are above the moving stage.In this disclosure the first arrangement is described as scanned-headCaliper AFM, and the second arrangement is described as the fixed-headCaliper AFM with scanned sample stage. Several specific alternativeCaliper AFM embodiments that take advantage of different probes andsample stage arrangements will be described later in this disclosure.

Although the disclosure of the present invention is discussed in termsof an atomic force (e.g., the van der Waals force), other interactionforces commonly used in scanning probe microscopy may also beapplicable. Examples of such other interactions include electrostaticforce, magnetic force, and tunneling current.

Use of Tilted Probes

Tilted probes for use in a Caliper AFM are described. Use of tiltedprobes raises issues related to clearance and positioning of theoscillators to allow their tips to be in proximity of each other ortouch each other as the oscillators are tilted and brought laterallynext to each other. The issues related to probe tilting are discussedfor the more restrictive case of tip-to-tip touching.

It is known to those skilled in the art that each AFM probe consists ofan oscillator that acts as a force sensor, a tip whose apex is engagedin interacting with the surface, and an oscillator mounting chip thatcarries the oscillator and facilitates its attachment to a motion stage.Conventional AFMs and their conventional oscillator mounting chips,oscillators, and tips have been designed to operate on a relatively flathorizontal surface and are not best suited for use as a Caliper AFM asdescribed in the disclosed invention.

A conventional vertically oriented AFM probe with sharp conical tipcould not interact with (for example, image or measure) a vertical orre-entrant sidewall of a sample with its apex. A conventional AFMoperating over a vertical surface will completely miss any near verticalsidewall surfaces in which the half-cone angle of the tip is larger thanthe slope of the sidewall. For a vertical sidewall the half-cone angleof the tip is always larger than the slope of the sidewall. Reentrantsidewalls are also inaccessible by vertically oriented probes with sharpconical tips

In another embodiment of the Caliper AFM at least one probe is tiltedaround an axis to enable better access of the tip to a vertical orre-entrant sidewall of a sample, as illustrated in FIG. 8. It is impliedthat the tip apex, and not the entire tip, needs to access the sample.Tilting the probe in more than one axis may enable better access of thetip to the sample. Tilting of both probes may be desirable.

Similarly, two conventional vertically oriented probes with sharpconical tips could not image or measure the same nanometer sized samplefeature at about the same time. It is implied that the tip apexes, andnot the entire tips, are engaged in operating on the sample. The widthof the oscillators would prevent the probes from working in proximity toeach other since the oscillators would collide before the tips are insufficient proximity to operate on the same nanometer sized feature atabout the same time. In practice, the sample features in the currentgeneration of semiconductor circuits are less than 250 nm wide,requiring that the tips also be less than 250 nm apart.

In another embodiment of the Caliper AFM at least one probe is tiltedaround an axis to enable better access of the two tips to the samenanometer sized sample feature at about the same time. Tilting the probein more than one axis may enable better access of the two tips to thesample. Tilting of both probes may be desirable.

In an extreme case, two conventional vertically oriented probes withsharp conical tips could not touch each other to implement azero-reference calibration procedure that is described elsewhere in thisdisclosure of the invention. However, the width of the oscillators wouldprevent the probes from touch each other since the oscillators wouldcollide before the tips are in sufficient proximity to touch.

In another embodiment of the Caliper AFM at least one probe is tiltedaround an axis to enable the two tips to touching each other. Tiltingthe probe in more than one axis may enables better access of the twotips to the sample. Tilting of both probes may be desirable.

Oscillator Clearance

For the best result, three tilts may be combined to enable the requiredclearance, as illustrated in FIG. 9. Lowering of the oscillator tip downwith respect to its base (Tilt 2) is typical with commercial AFMs and isintended to provide clearance for clamping of the base of theoscillator. One-sided oscillator clamping can eliminate the need forTilt 2. Rotating each oscillator around its long axis (Tilt 1) enablesaccess to the feature sidewalls. Clearance with respect to the sample isrequired to avoid crashing of the oscillator's edges into the sample.Oscillator and base width, together with tip length, control the degreeof Tilt 1. It is desirable that the Tilt 1 is larger than the half-coneangle of the tip. Experimental results have shown that acceptable Tilt 1is about 10 degrees for a half-cone tip angle of 10 degrees. Pivotingeach oscillator around its tip axis (Tilt 3) and pivoting their basesaway from each other allows for side-to-side oscillator proximitywithout crashing the edges of the oscillator with respect to each other.Relocation of the position of the tip with respect to the oscillator andbeveling of the oscillator's ends enable Tilt 3.

Oscillator Tilt Adjustment

In one embodiment of the caliper AFM, all three oscillator tilts can befixed at set-up. In another embodiment, to enable access to a range ofvertical and reentrant sidewalls with a standard conical sharp tip, Tilt1 is adjusted at set-up with the help of an angular stage, while Tilt 2and Tilt 3 are fixed. However, the adjustable tilt, Tilt 1, remainsfixed during scanning. Adjustable Tilt 1 is particularly needed forimaging and measurement of dense lines with high aspect ratio andreentrant sidewalls, where Tilt 1 has to be have a certain value toreach the bottom of the features and access the sidewalls.

Compact Angular Stage Embodiment

The preferred embodiment of a new compact angular stage design isdescribed. Referring to FIG. 10, the circular arc bearings 1001 and 1002are concentric with a point at the probe tip apex, 1003. An actuator,illustrated as a drive wheel, 1004, is provided to rotate the angularstage. Support elements, illustrated as rollers, 1005 and 1006, maintainthe circular arcs in a concentric relationship with the probe tip apexbefore, during and after rotation. The smoothness and eccentricity ofthe inner and outer arcs will be critical for achieving tilts with veryhigh precision. Also of concern are dimensional tolerances for theconcentric arcs and support bearings, and the effect of structuraldeformation under loading by the bearings. This embodiment maintains theprobe tip apex at a specified location while rotating the probe and itssupport structure through a specified angle. Clearance with respect tothe sample is required to avoid crashing of the oscillator's edges intothe sample. The preferred embodiment achieves clearance by havingbeveled left and right bottom surfaces 1007 and 1008, to provideclearance with respect to the sample as the oscillator is tilted.

Reduction of the pitch angle of the angular stage with respect to thesample is desired because it increases the available tilt range.Preferably, the angular stage has zero pitch angle, in which case thelong axis the AFM cantilever is parallel to the sample plane. Attachmentof the cantilever to the base of the angular stage may take into accountthat an excitation PZT needs to be mounted between the bottom of thestage and the oscillator base.

An embodiment of the angular tilt stage can be manufactured to bemillimeters in size and be able to tilt through angles on the order of ∀10< as may be required to enable the probe tip to access undercuts ofdense high aspect-ratio features. An embodiment of the angular stage canbe mounted on a PZT-based XYZ scanning stage.

The preferred embodiment has an integrated tilt sensor to providefeedback for controlling the tilt. One embodiment uses external PZTdrives with integrated sensors to precisely actuate the angular stageand sense the amount of tilt. With this approach, the tilt is translatedinto linear displacement through levers. Another embodiment uses afiducial mark on the oscillator surface to read out its tilt. In thisembodiment, the reflection off the fiducial is read with a PSD detector.

For some applications, it may be necessary to decouple angular motion ofthe tilt stage from linear translation of an XYZ stage on which it ismounted. This can be accomplished by providing feedback from the tiltsensor to both the XYZ stage and the tilt stage so as to maintain theapex of the tip at a fixed position. The feedback loop can providedynamic response in case high angular accelerations are required fortilting as well as means for fine tuning of the rotation axis tocompensate for tip wear.

Tips for Use with Caliper AFM

Each probe includes a tip. The choice for a probe tip for a caliper AFMcan depend on the application. In an embodiment for a Caliper AFM formeasuring and imaging of isolated features, tip requirements areminimal. A common conical silicon tip with height of a few microns,full-cone angle up to 20°, and tip radius of 10 nm is sufficient. Theseapproximate tip dimensions enable access to the sidewalls of the featurewith tilted tips.

In another embodiment of a Caliper AFM for measuring and imaging of moredemanding applications, such as linewidth measurement of dense, highaspect ratio lines with reentrant sidewalls, a sharp tip may be used toenable accessing the bottoms of the trenches and the undercuts of thesidewalls. Such a tip may have full cone angles of 3 to 6 degrees toaccess dense features down to 100 nm size with corresponding trenches of100 nm that actually limit the tip access. The tip length can be high,10 microns or more, to allow oscillator tilts through large angles,∀25°. Using sharp 1-D silicon tips to access vertical and highlyreentrant sidewalls to take CD measurements is feasible. Commerciallyavailable sharp tips that are ion milled down to a full cone angle of 10degrees can be used, for example.

Carbon Nanotube Tips

In another embodiment of a Caliper AFM, carbon nanotube tips can be usedfor linewidth measurements of features that are less than 100 nm. Theadvantage of carbon nanotube tips is that that they are small andslender.

Polystyrene Bead Tips

One important aspect of tips is their apex radius. It may be beneficialfor the tips to be approximately identical to each other so as toprovide symmetry during the zero reference calibration process in whichthe tips touch each other at their apexes. In another embodiment for aCaliper AFM, polystyrene beads may be attached to the apexes of thetips. Polystyrene beads are perfectly symmetrical spheres with diametersof less than 1 micron. Use of spherically terminated tips may tend toeliminate tip uncertainties.

Scanning Along Vertical Sidewalls

For linewidth measurement of features in semiconductor circuits it isdesirable that an AFM be able to image and measure vertical andreentrant sidewalls. One limitation of conventional AFMs is theirinability to scan along vertical surface walls, mainly due tolimitations of the force sensor, including the cantilever. Otherlimitations are due to the tip shape. Conventional AFMs use only themain cantilever (first bending) resonant mode and are therefore able torespond to tip-surface forces from a horizontal surface. This impliesthat conventional AFMs scan only in the horizontal direction. One priorart AFM used for critical dimension measurements has a boot-shaped tipthat allows access to vertical and reentrant sidewalls and it dithersits cantilever in the lateral direction (frequency modulated on top ofthe main cantilever resonant mode) to enable it to respond totip-surface forces from a vertical surface and therefore scan in thevertical direction. One of the shortcomings of the lateral dither isthat it is not a resonant cantilever mode and therefore provides forcesensor sensitivities that are not adequate. Another shortcoming is thatthe dither is dependently coupled to the bending mode to deliver forcesensing.

A more suitable solution for a Caliper AFM is the use of probe tiltingto enable tip access to vertical and reentrant sidewalls and use ofmultiresonant oscillators with superior force sensitivity fortip-surface forces due to both, horizontal and vertical surfaces.

Multiresonant Oscillator

The multiresonant oscillator is a new type of AFM cantilever withgreatly enhanced lateral force sensitivity. It can be called amultiresonant oscillator, instead of a cantilever, because it isdesigned to respond in two or three resonant modes that produce tipmotions that are orthogonal to each other. Each resonant mode isprimarily sensitive to a different component of the surface forcegradient acting on the vibrating tip. Vertical force sensitivity allowsscanning in the horizontal direction (classical AFM mode) and lateralforce sensitivity allows scanning in the vertical direction. Design ofthe oscillator's shape, thickness, and width promote the desiredfrequency signature of the respective resonant modes. By tuning theoscillator design one can achieve vertical and lateral forcesensitivities that are comparable to each other. Therefore, tip controlis superior in both scan directions. The inputs to a feedback controllerare the shifts in the two selected resonant frequencies of theoscillator in response to a surface force gradient component in thecorresponding direction. The outputs of the feedback controller providesignals to the scanning stage, which it uses to keep the tip-to-sampledistance fixed (measured along an effective tip-to-surface normal).

Touch Probing

It is clear from Equations (1) and (3) that linewidth uncertainties canbe reduced or eliminated by taking away the effect of the tip-surfaceinteraction. One way to remove the effect of the tip-surface interactionis to operate the AFM in a contact mode of operation. Contact moderelies on short-range (sub-nanometer) attractive surface forces andrequires no modeling of the tip-surface attractive interaction. However,scanning in contact mode can rapidly degrade both the tip and thesample. Non-contact mode depends on the long-range conservative surfaceforces that can strongly depend on surface contamination and can varywith the material composition of the sample. This dependence makes thenon-contact mode of operation also prone to variations and thereforegreater uncertainties.

A method of tip-surface interaction that is disclosed in this inventionis a touch-probing method of operation. Touch-probing is defined as aspecial kind of a repulsive (contact) mode of tip-surface interaction.It has to be noted that during the touch-probing process there is noscanning (zero scan velocity), therefore, this is can be a gentleprocess that will not cause tip or sample degradation. In a conventionalcontact mode of scanning, the tip can be dragged along the surface (nonzero scan velocity) while in contact with the surface, possibly causingunwanted damage to itself and the sample. The touch-probing method issuitable for a conventional AFM operation and a Caliper AFM operation.

Alternating Scanning Mode

A better way of operating a Caliper AFM is the combined use of twodifferent scanning modes, non-contact mode scanning, for localnavigation of the probes with respect to the sample, and touch-probingof the two tips with respect to the sample to obtain the requireddimensional measurement. The combined use of two different scanningmodes is referred as alternate scanning mode, implying that the twodifferent modes are used in alternating manner.

The combined use of non-contact mode scanning and touch probing is bestutilized if it is integrated with other technological advances such asscanning along vertical sidewalls and a logic and feedback controller.

Another embodiment of the Caliper AFM uses an alternating scanning mode.During non-contact mode of scanning, in both the horizontal and verticaldirections, the tip can be held at an operational nanometer-scaledistance from the sample, consistent with the long range of theattractive van der Waals forces. In some implementations, the amplitudeof vibration of oscillator and tip in non-contact mode may be about 1 nmin the two orthogonal directions. Constant phase or amplitude may beused to keep the tip-to-surface distance at its operational point. Afterclimbing the tip to a desired feature height, the non-contact mode ofoperation in vertical scanning may alternate with a touch-probe(contact) mode of operation. There may be two ways to do the modeswitching. In the first switching mode, while the system is in anon-contact mode of operation, the reference point of the controller maybe biased to set the tip-surface distance to a sub-nanometer distanceand therefore drive the tip into the repulsive surface force region.This action will cause snapping of the tip to the surface. While incontact the tip will still vibrate. At this point the vibrationexcitation may be ceased in order to determine the DC position of thetip with respect to the sample. After the measurement has been taken,the procedure may be reversed in the same order to resume non-contactscanning. In the second switching mode, while the system is innon-contact mode of operation, the vibration excitation may be ceasedfirst, followed by a DC approach of the tip to the sample, until contactis established. There may be some settling time after the vibration isceased for the oscillator to be settled and before the tip approach isapplied. Again, there may be snapping just before the tip and thesurface are in contact. After the measurement has been taken theprocedure may be reversed in the same order to resume non-contactscanning. Restarting the vibration and going back to the originalreference point of the controller, to set the tip-surface distance to becompatible for non-contact mode of operation, may cause someovershooting of the tip-sample distance, which could settle out fastdepending on the feedback control. After the overshooting has beenstabilized the non-contact scanning may resume. The first method ofswitching provides dynamic mode alternation while the second mode ofswitching provides quasi-static mode of alternation.

Other issues that may arise during the mode switching are elasticinteraction between the tip and the surface, snapping of the tip to thesurface that may cause static bending and torsional deflections,settling times during switching, simultaneity of the switching betweenthe two tips, and the repeatability of the switching back to non-contactmode

In one embodiment, after clearing the top of the sample, the two tipstouch each other again to establish the zero reference point. The sameswitching technique may be employed here to go from non-contact totouch-probing mode of operation.

Transverse Mode of Scanning

Referring to FIGS. 11-14 in one Caliper AFM embodiment a transverse modeof scanning is the preferred mode of scanning. In such embodiment, twosharp silicon tips and the AFM probes supporting them are rotated inspace with up to three degrees of freedom, as illustrated in FIG. 11, soas to provide adequate clearance and feature access during thesubsequent measurement sequence. The tips are then commanded to engagethe direct contact, touch probe mode and then translated in a way thatallows them to touch each other at their respective lateral extremepoints, thereby establishing a zero-lateral-distance reference. This isthe pre-measurement calibration step performed in one dimension, i.e.,the lateral direction. The caliper tips are then opened to accommodatethe feature and positioned at its right and left sides. The tips arethen caused to approach the base of the feature, using non-contact modescanning for local navigation. The tips encounter the lower corners ofthe feature and then start to climb the sidewalls, which may be verticalor even highly reentrant. Multiple resonances of the oscillator and aspecial sensing system may be used to achieve the 2-D force sensingneeded to scan the tips horizontally as well as vertically. During thenon-contact mode of scanning in both horizontal and vertical directions,the tip is kept at a constant nanometer-scale distance from the sample,consistent with the long acting range of the attractive van der Waalsforces. At desired heights of the feature the vertical scanning ishalted, the non-contact mode of operation is turned off, and therepulsive, contact mode of operation, with zero scan velocity, is turnedon. Once the tips touch the sample the linewidth measurement is made.The lateral positions of the two probes and their relative distance arerecorded by the sensing system to establish the feature profile and thelinewidth measurement. After the linewidth measurement is obtained, thetouch-probing mode of operation is turned off and the non-contact modeof operation is turned on. The tips resume non-contact mode scanning andnavigate to the next measurement point. After they clear the top of thesample the tips again are operated in touch probe mode and are moved totouch each other at their respective lateral extreme points tore-confirm the zero reference.

Longitudinal Mode of Scanning

In an alternative mode of scanning, the tips may be scanned in thelongitudinal direction, at fixed feature height, along the length of thefeature, as illustrated in FIGS. 12, and 13. The principle of operationof this longitudinal scanning is the same as that for transversescanning described above, except for the direction of scanning. Theadvantage of longitudinal scanning is that the scanning speed can besignificantly improved since the tips do not have to switch scandirections all the time.

Via and Contact Hole Scanning

In another alternative mode of scanning an embodiment of the caliper AFMcan be used to image vias and measure their width. This is, in fact, anegative linewidth measurement. Because of the clearance issues, forthis type of scanning the tips may need to be inserted into the via oneby one. As with any scanning mode, the zero reference point can beestablished by touching the tips with respect to each other.

Sensing

Vibration Sensing System

The function of an AFM vibration sensing system is to convert a timedependent force sensing response of a cantilever interacting with asurface into information fed to a controller that adjusts the tip tosample distance. The output of the vibration sensing system is an ACsignal with a frequency that matches the resonant frequency of thecantilever. It can be noted that a multiresonant oscillator used in anembodiment of the disclosed invention accomplishes force sensing in twomultiple mutually orthogonal directions. This implies that for amultiresonant oscillator there will be two output signals withfrequencies that match the resonant frequencies of the multiresonantoscillator.

An embodiment of the Caliper AFM consists of a vibration sensing systemresponsible for monitoring the response of the oscillators as theyinteract with the surface of the sample or as their tips interact toeach other. There are numerous ways to accomplish the vibration sensingtask for a Caliper AFM. Few examples are outlined.

In one example, there are two vibration sensing systems, one for eachoscillator, and in another example there is a single vibration sensingsystem for both oscillators. In one example, two vibration sensingsystems monitor two resonances of a single multiresonant oscillator andin another example there is a single vibration sensing system for bothoscillators resonances.

In one example, the vibration sensing system is a laser-bounce basedsensing system in which a focused laser beam pointed towards theoscillator and where a detector monitors the vibration of a reflectedlaser beam. In another example, the vibration sensing system is aninterferometric system.

For a Caliper AFM embodiment with stationary probes and scanned samplethe vibration sensing system consists of two separate vibration sensingsystems, one for each oscillator. The vibration sensing system of thisembodiment is a laser-bounce based sensing system where the laser sourceis fixed with respect to the oscillator and the detector is a positionsensitive detector (PSD) or a continuous PSD.

In one Caliper AFM embodiment with scanned probes and stationary sample,the vibration sensing system consists of two separate vibration sensingsystems, one for each oscillator. In this vibration sensing system theuse of a fixed focused laser source is not applicable for vibrationsensing of a scanned oscillator because the focused laser spot couldfall off the oscillator as it is scanned in X and Y and could de-focusas the oscillator is displaced in the Z direction. Two possibleapproaches to accommodate vibration sensing of a scanned oscillatorinclude (a) a focused laser source that scans together with theoscillator or (b) to use a fiducial mark on the surface of theoscillator and a fixed collimated laser beam to monitor the vibration ofthe oscillator as it scans. The first approach is self-explanatory andwill not be discussed. The second approach will be discussed.

Fiducial Marks for Vibration Sensing

In one embodiment of the Caliper AFM, illustrated in FIGS. 15 and 16,the use of a fiducial mark for vibration sensing eliminates the need fora focused light beam. One implementation of the fiducial mark is areflective mark surrounded by a non-reflective region of the oscillatorsurface. A collimated incident beam generates a reflection from thefiducial mark. This reflected beam is incident on the aperture of aposition sensitive detector (PSD). Vibrations of the oscillator willcorrespond to vibrations of the fiducial mark that can easily becaptured by the PSD regardless of the X, Y, Z alignment of theoscillator with respect to the collimated beam as long as the fiducialmark is inside the area of the collimated beam.

Vibration Sensing of Multiresonant Oscillators

In another embodiment of the Caliper AFM there is a single vibrationsensing system for both oscillators' resonances. Regardless of the waythe reflected light beam is generated, for example, from a fiducial orwith a focused laser beam, the method of detecting multiple resonancesfrom a multiresonant oscillator with a single PSD is the same. Thevibration sensor signal is an AC signal that depends on the amplitude ofthe laser spot anywhere on the aperture of the PSD, and it may beproportional to the vibration of the oscillator. Any number ofresonances can be monitored with a single PSD by frequency demodulatingthe AC signal from the PSD. Detecting multiple oscillator resonanceswith a single PSD is feasible.

Stage-Independent Position Sensing

Direct measurement of the tip-to-tip differential distance is anotherindependent way to remove uncertainties in a linewidth measurement withscanned dual probes. One solution to the problem is to come as close tomeasuring the actual tip position as possible. In this solution, the XYZposition of the probe is obtained from the scanning stage sensors and anassumption is made that there are no other relative displacementsbetween the stage and the probe. The stage position is then used toinfer the probe position and, with that, the sample topography.

Another solution is to directly measure the tip-to-tip distance. In oneCaliper AFM embodiment there is a single vibration sensing system forboth oscillators. This caliper AFM embodiment is suitable for directtip-to-tip measurement to eliminate mechanical loop uncertainties.

Direct detection of the oscillator itself removes the sensingrequirement from the scanning stage and makes it a responsibility of thescanning sensor. Direct measurement of the differentialoscillator-to-oscillator distance can provide the differentialtip-to-tip distance. Referring to Equations (4) and (5) we cansubstitute the stage position measurements with tip positionmeasurements to obtain the linewidth measurement:w _(differential) =K[(y _(tip) −x _(tip))−(y _(Rtip) −x _(Rtip))]  (8)w _(differential) =K[Δ _(tip)−Δ_(Rtip)]  (9)where K is a scaling factor. Reliance on the stage measurements withrespect to a reference structure assumes that there are no vibrations ordrifts in the mechanical chain from the stage to the tip. The stages maybe able to guarantee that the measurements y and x are stable, but thereis no guarantee that the stage-to-tip distances are stable. On the otherhand, the position of each fiducial, y_(tip) and x_(tip), is as close tothe tip as possible and can be considered very stable and insensitive tovibration or drift. Use of a single detector to monitor the differentialmeasurement y_(tip)−x_(tip) addresses mechanical instabilities betweentwo separate detectors.Stage-Independent Position Sensing with Fiducial Marks

Another embodiment of the Caliper AFM employs fiducial marks forimplementing stage independent position sensing of the scanned probes.Fiducial marks attached to the free ends of the respective oscillatorscan be used to detect the in-plane (XY) and out-of-plane (Z) position ofthe oscillators themselves, without relying on the scanning stage sensorfor that information. Change of the XYZ position of the oscillator, andwith it the fiducial, can cause traversing of the reflected light beamon the aperture of the PSD that is proportional to the XYZ position ofthe oscillator. By locking any of the two axes the third one can bedirectly detected. Position change of the fiducials can manifest itselfas a change of the DC output of the PSD. For linewidth measurements, Zand Y may be locked as to produce a DC signal that is proportional tothe position of the oscillator in X direction.

Stage-Independent Position Sensing with Focused Light Beam

Another embodiment of the Caliper AFM employs fixed focused laser sourcefor implementing stage independent position sensing of the scannedprobes. In this embodiment the reflected light beams from twooscillators (from the Caliper AFM) is directed with the help of mirrors,and collimators if needed, towards the aperture of a single detector. Itis preferred if the detector is a continuous PSD detector. The principleof detecting the relative position of two laser spots on a singleaperture was described before.

Vibration and Position Sensing of Two Scanned Probes with a Single PSD

The decision to use vibration and position sensing of two scanned probeswith a single PSD is used in another Caliper AFM embodiment, illustratedin FIG. 4. Use of fiducial marks for position sensing poses thepotential of using the same fiducial mark for vibration sensing.Electronic signal processing can be implemented to simultaneouslymonitor oscillator vibration (AC) and position (DC). The AC component ofthe signal will be proportional to the vibration of the oscillator andthe DC component of the signal will be proportional to the in-planeposition of the oscillators. The AC signal may be further processed andsent via a feedback signal to the scanning stages to maintain constanttip-sample distance. The DC signal can be used to monitor the positionof the oscillators with respect to their initial positions.Simultaneously monitoring vibration and position of a laser beam with asingle PSD is feasible. In some implementations, the signal-to-noiseratio of this signal processing may be poor. Two oscillators couldproduce two reflected laser beams that hit the aperture of a single PSD.Using light intensity multiplexing, a single PSD can simultaneouslyprocess two independent laser beams that correspond to two oscillators.Each reflected beam carries within itself the vibration and positioninformation of the respective oscillator. After they are separated bydemodulating the incoming signal, the AC (vibration) and DC (position)components of each signal can be processed in a manner consistent withabove described signal processing requirements. The relative differenceof the DC component of each signal will be proportional to theoscillator-to-oscillator (tip-to-tip) distance.

Sensing System for a Caliper AFM

In a specific example, illustrated in FIG. 4, we describe how a sensingsystem works for a Caliper AFM embodiment. Collimated light from awide-beam laser is pointed towards the two probes. Typically acollimated laser beam is 1 mm in diameter while scan areas may vary from2:m×2:m to 100:m×100:m. However, the diameter of the beam is limitedonly by power. The fiducial marks are reflective surfaces on anon-reflective background. Therefore, illumination by a collimated beamwill produce a collimated reflective beam. The use of fiducial markseliminates the need to use a focused laser beam that tracks theoscillators so as to keep its focal point within a region on theoscillator surface. For a dual-probe design there will be two reflectedbeams, each pointing opposite of each other, consistent with the spatialorientation of the oscillators. A set of fixed mirrors can be used topoint the reflected laser beams into the aperture of the PSD. Althoughideally collimated, these reflected beams may be slightly diverging.Therefore, the optical paths from the fiducials to the PSD should bekept as short as possible, e.g., in a cm range. The preferred positionsensitive detector is a continuous type of position detector. Using asignal processing technique the PSD will process two input signalssimultaneously. The AC components of the signal will be proportional tothe vibration of the oscillator and the DC components of the signal willbe proportional to the in-plane positions of the oscillators. The ACsignal is further processed and sent via a feedback signal to thescanning stages to maintain constant tip-sample distance. The mainbending resonance will provide most of the sensitivity required forhorizontal scanning and the torsional resonance will provide most of thesensitivity required for vertical scanning. The DC signal will be usedto directly monitor the positions of the oscillators with respect totheir initial locations. The relative position of the two oscillatorswith respect to each other will provide a scaled measure of theoscillator-to-oscillator (tip-to-tip) distance. By contrast, thepositions of the scanning stages will also provide information about theoscillator-to-oscillator distance, but indirectly. This contrast ofdifferent types of differential distance measurement is discussedelsewhere in detail.

Stage-Independent Position and Tilt Sensing with Fiducial Marks

Another embodiment of the Caliper AFM employs fiducial marks forimplementing vibration sensing as well as stage independent position andtilt sensing of the scanned probes. An example of a measured tilt is thevariable Tilt 1 or the compact angular stage as described elsewhere inthis invention. In this embodiment the sensing system is using scannedoscillators with fiducial marks to determine their in-plane position andout-of-plane tilt during scanning. The size of the collimated beam hasto be at least the size of the scanned area. Typically a collimatedlaser beam is 1 mm in diameter while scan areas may vary from 2:×2: to100:×100:.

The stage-independent scan sensing and its simultaneous use with thetilt and vibration sensor can be achieved with the use of a sensinglogic. This innovative method assumes use of a fiducial mark and asingle PSD for the entire sensing operation. Any other combination offiducial marks, focused laser, single or dual detectors is alsoapplicable for the disclosed method. The vibration sensor signal is anAC signal that depends on the amplitude of the laser spot anywhere onthe aperture of the PSD, and it is proportional to the vibration of theoscillator. Any number of oscillator resonances can be monitored with asingle PSD by frequency demodulating the AC signal from the PSD. Thetilt sensor signal is a DC signal that depends on the position of thelaser spot on the aperture of the PSD, and it is proportional to thetilt of the oscillator. The scan sensor signal is a DC signal thatdepends on the position of the laser spot on the aperture of the PSD,and it is proportional to the XYZ position of the oscillator. Bystrategically positioning the PSD with respect to the reflected lightfrom the fiducial one can achieve the desired signal distribution. Thereare five unknowns; X, Y, Z, tilt position, vibration amplitude, and only2 outputs from the PSD, Xpsd and Ypsd. To make up for lack ofinformation the method uses, at the same time, only enough signals as wecan resolve, any two positions and a vibration. For example, duringscanning, X and tilt are fixed and we monitor Z, Y, and vibration.During rastering, Z and tilt are fixed and X and Y are monitored.Therefore, it is possible to use combinations 1 or 2 or 4 with 3.

Redundancy of the measurements can be obtained, if necessary, by addingan extra fiducial mark, an extra focused laser beam, or an extracollimated beam. However, this addition increases the complexity andsize of the scanned AFM head.

Caliper AFM Navigation

Another embodiment of the Caliper AFM employs use of the fiducial markto simplify the site navigation and improve the coarse positioning toprecisely determine the starting point of the AFM scan. This embodimentoffers significant improvement in throughput due to improvements of thenavigation process.

In this embodiment the fiducial mark on the oscillator is used as aregistration mark that can be used with optical pattern recognitiontechnology to greatly improve site navigation. In another embodiment,the same fiducial mark that is used for navigation can also be used forvibration, position, and tilt sensing. The fiducial mark is a verydistinguishable feature on the oscillator that is not ambiguous, as isrecognition based on an edge of an oscillator. With this approach, priorknowledge of the IC design and a registration mark on the wafer are usedto determine relative positioning of the fiducial mark with respect tothe wafer, and therefore the tip of the probe, even if the sample isfully occluded by the oscillator. This independent sensing andpositioning capability in lieu of coarse-mode pre-scanning to find thestarting point of the measurement can be achieved with nanometerprecision. With the help of the in-plane stage-independent sensingcapability, one can control the oscillator's XY position with nanometerprecision within the range of the scanning stages. With the help of thevibration, position, and tilt sensing method described elsewhere, thetilt and the Z displacements of the oscillator need to be kept fixedwhen the oscillator moves in the XY plane. If Z displacement is needed,the XY position can be fixed and the Z position of the oscillator can besensed. Again, one needs prior knowledge of the IC design and aregistration mark on the wafer to position the fiducial mark withrespect to the wafer registration mark. If some pre-scanning is stillneeded it will be extremely minimal.

Another embodiment of the Caliper AFM employs use of the fiducial markto simplify the site navigation and improve the coarse positioning toprecisely determine the starting point of the AFM scan, wherein thefiducial mark is located on the mounting chip itself or a feature of themounting chip, such as its bevel, may be used as a fiducial. In thisapproach the fiducial is no longer tied to the oscillator and cannot beused for force sensing.

Another embodiment of the Caliper AFM employs use of angular tilt of theoscillators to remove the occlusion of the sample by the oscillator andto use that view to navigate the oscillators to a position ready forscanning. In this approach the oscillator is tilted through angles thatare large enough to enable observation of the probe tip from a top downview but not as much tilt as into crash the probe to the sample. Sincethe typical half-width of an oscillator is 15: and a typical tip can be15: long, one needs about a 45< tilt to achieve this goal.

Control

Controller

An embodiment of the caliper AFM includes at least one controller thatcontrols the tip of each probe with respect to the sample, and eachprobe with respect to the other. In one example, the controller is aconventional PID feedback controller. In another example, the controlleris a multiple-input-multiple-output (MIMO) feedback controller. Inanother example, the controller is a real-time controller. In anotherexample, the controller is a digital controller. In another example,there are two controllers, one for each probe. In another example, thereare two controllers, one for each resonant mode of a single oscillator.In another example, the sample stage also has a controller. In anotherexample, there is a logic that connects the multiple controllers.

In one embodiment of the Caliper AFM the controller is a real-time,digital, multiple-input-multiple-output (MIMO) feedback controller, onefor each probe, and a logic that coordinates the two MIMO controllers. AMIMO controller is better than two or more PID controllers since itintegrates the function of two PID controllers and takes into accountany cross-talks. The MIMO controller of a single probe is responsiblefor scanning the probe in 2-D, on a horizontal surface (verticalscanning) and on a vertical surface (lateral scanning). The inputs tothe MIMO feedback controller for each probe are responses of twoselected resonant frequencies of an oscillator. These responsescorrespond to the two selected modes, which respond so as to move thetip in two primarily orthogonal directions as the tip interacts with thesurface. The outputs of the MIMO controller for each probe providesignals to the XYZ scanning stage which keeps the tip-to-sample distancefixed (measured along an effective tip-to-surface normal) in verticaland horizontal direction. Coordination between the two individual MIMOcontrollers may be needed. Each MIMO controller benefits from beingaware about the situation of the other MIMO controller so as tocoordinate the scanning and so as not to damage the sample or run theoscillators into each other. Although each MIMO controller would bededicated to an individual oscillator in this embodiment, a delay andtrigger loop in the MIMO controller can ensure that one MIMO controllerdoes not take action without first checking with the other MIMOcontroller. Software logic can furnish this checking capability. Adigital controller would benefit implementation of the MIMO controller,since it can handle a more complex algorithm than an analog controller.LabView based hardware and software are candidates for this task, forexample.

In another embodiment of the controller, two integrated MIMO feedbackcontrollers can provide tip-to-tip feedback control. Coordinationbetween the two MIMO controllers may be integrated in the feedback. OneMIMO controller (the “leader”) scans one oscillator in response to thedisturbance from the surface. The second MIMO controller (the“follower”) scans the second oscillator in response to the disturbancefrom the surface and the relative distance to the other oscillator. Morecomplex MIMO control can accomplish this task. Non-linear responses mayhave to be accounted for.

Method of Operation of Caliper AFM

Measurement Using a Caliper AFM

The method of measurement using a caliper AFM is illustrated in FIG. 17.The tips of left and right AFM probes are positioned on the surface of afeature. In this illustration, the feature is stationary relative to atool-fixed reference frame, XYZ. Probe-fixed reference framesX_(L)Y_(L)Z_(L) and X_(R)Y_(R)Z_(R) are attached to the left and rightprobes respectively, and move with the respective probes. Points L and Rare the origins of the respective reference frames. In general, theprobe tips may have different shapes and sizes.

A region near the apex of the left probe tip is illustrated in FIG. 18.If the feature sidewall is vertical, then only the extreme lateral pointof the left probe tip contacts the sidewall. Similarly, if the featuretop is horizontal, then only the extreme vertical point of the leftprobe tip contacts the top. In a more general situation, the featuresurface presents a range of angles to the tip, and any point within anarc near the tip apex may come into contact with the left sidewall andtop of the feature as the position of the left probe changes withrespect to the feature. In a three-dimensional representation, thelateral and vertical extreme points and the arc are located on thesurface of the tip by specifying their three coordinatesX_(L)Y_(L)Z_(L).

A relative measurement occurs when the probes are positioned withrespect to the feature in a coordinated manner and a sensing system isused to assign values to coordinates that specify the position andorientation of one probe relative to the other probe. Sensing theposition and orientation of one probe relative to the other while theprobe tips are in contact with the feature surface, together withknowing the locations of the respective arcs, in the probe-fixedreference frames, provides the information needed to determine adimension of the feature.

If the arcs can be replaced by extreme lateral points, as in the case ofvertical feature walls for example, the feature dimension can bedetermined by straightforward arithmetic computations. If finite sizearcs may contact the feature during the measurement, then adeconvolution procedure is required to remove the effect of probe shapeand recover the feature dimension. However, even if a deconvolutionprocedure is needed, the caliper architecture confines the required arcto a relatively small region near the apex of the tip, rather thanrequiring it to extend over the entire tip, as when a single probe withfixed orientation is used to contact both sides of a feature. In thecase of a caliper AFM, using sharper tips can shrink the required arcsto arbitrarily small sizes, as illustrated in FIG. 19, without requiringreorientation of a probe through a large angle so as to allow it toaccess both sides of the feature during scanning. In the case of asingle probe AFM, however, using a sharper tip can only shrink therequired arc to an arbitrarily small size if the single probe isreoriented through a large angle during scanning so as to allow it toaccess both sides of the feature. Reorienting an AFM probe through alarge angle during scanning is typically not done because it requiresconsiderable effort to design and build a system that prevents theaccompanying rotational motion from coupling into the linear motion andthereby corrupting the measurement data.

A globally referenced measurement occurs when one of the probes ispositioned with respect to the feature and a sensing system is used toassign values to coordinates that specify its position and orientationin relation to the tool-fixed frame XYZ. For example, sensing theposition and orientation of the left probe-fixed frame X_(L)Y_(L)Z_(L)with respect to XYZ, together with knowing the location of the arc inthe left probe-fixed frame, provides the information needed to determinethe location of a point in contact with the left side or top of thefeature in relation to XYZ. Similarly, the right probe can be used tomake a globally referenced measurement of a point in contact with theright side or top of the feature in relation to XYZ. Combining two suchglobally referenced data sets resulting from measurements made atmultiple points can produce an image of the feature, i.e., arepresentation of its size and shape in relation to the tool-fixedframe. Using a caliper AFM also enables combination of a globallyreferenced measurement with a relative measurement so as to both createan image of the feature and determine its size. For example, the leftprobe can be used to generate an image of the left side and top of thefeature with respect to XYZ, as described above, while the right probeis coordinated so as to make measurements on the other side of thefeature while its position and orientation are being sensed with respectto the left probe.

Using a caliper AFM also enables combination of two globally referencedmeasurements so as to both create an image of the feature and determineits size. For example, the left probe can be used to generate an imageof the left side and top of the feature with respect to XYZ, asdescribed above, while the right probe is coordinated so as to generatean image of the right side and top of the feature with respect to XYZ. Astraightforward numerical computation performed on the two globallyreferenced measurement data sets can provide information about the sizeof the feature, e.g., its width at given values of Z.

Both transverse and longitudinal scans can be made using a caliper AFM.Any type of scanning path, including transverse and longitudinal scans,can be used to make either relatively referenced measurements orglobally referenced measurements or a combination of globally andrelatively referenced measurements.

A non-contact mode measurement can be made using a caliper AFM bycoordinating the probes so that they each attempt to maintain a presettip-sample distance, which may be called the fly height. This can beaccomplished, for example, by sensing an interaction force (e.g., thevan der Waals force) between the tip and the sample and using the sensedinteraction to control the fly height.

The left and right caliper AFM probes can be coordinated so that theymake either relatively or globally referenced measurements atapproximately the same time, or at different times. If measurements aremade at different times, then the resulting data sets can be recorded atthe time they are generated and later combined to generate images andfeature sizes.

Fixing at least one of the coordinates XYZ during scanning, and thenincrementing that coordinate prior to executing a subsequent scanresults in a type of scan called a raster scan. Fixing Y, for example,results in a transverse raster scan.

Calibration of a Caliper AFM

A caliper AFM can be calibrated using an artifact having a knowndimension, as illustrated in FIG. 20. For example, a globally referencedimage of the artifact (i.e., with respect to XYZ) can be generated bymaking measurements as the left probe scans the artifact. The knowndimensions of the artifact can then be used to deconvolve the shape ofthe artifact from the measurement data. This results in a determinationof the shape of the left probe tip. The X_(L)Y_(L)Z_(L) coordinates ofthe arc comprising points near the left tip apex that contact theartifact can then be adjusted. A similar calibration procedure can beperformed with the right probe tip.

Alternatively, a caliper AFM can be calibrated using, a relativelyreferenced measurement of an artifact (e.g., a measurement made withrespect to X_(L)Y_(L)Z_(L)). The known dimensions of the artifact canthen be used to establish a relationship between the X_(L)Y_(L)Z_(L)coordinates of the arc comprising points on the left probe tip thatcontact the artifact and the X_(R)Y_(R)Z_(R) coordinates of the arccomprising points on the right probe tip that contact the artifact, asillustrated in FIG. 21. A calibration using, a relatively referencedmeasurement of an artifact can be used to remove the effect of probeshape from relatively referenced measurement data so as to recoverdimensions of a feature (e.g., its width).

A caliper AFM can be calibrated using the lateral extreme points of thetips by using an artifact with vertical side walls, as illustrated inFIG. 22. Alternatively, A caliper AFM can be calibrated using theextreme vertical points of the tips by using an artifact with ahorizontal surface, as illustrated in FIG. 23.

A caliper AFM can be calibrated using an artifact having a knowndimension, while the tips are not in contact with the artifact, asillustrated in FIG. 24. The measurement of the artifact requiresknowledge of the fly height associated with an interaction force (e.g.,the van der Waals force) between the tip and the sample.

A caliper AFM can alternatively be calibrated using the lateral extremepoints of the tips by using an artifact with vertical side walls, whilethe tips are not in contact with the artifact.

A caliper AFM can alternatively be calibrated using the vertical extremepoints of the tips by using an artifact with a horizontal surface, whilethe tips are not in contact with the artifact.

Calibration of a Caliper AFM Using Tip-to-Tip Interaction

A caliper AFM can be calibrated by positioning the tips such that theyare at a known tip-to-tip distance for which they have a knowninteraction, as illustrated in FIG. 25. The known tip-to-tip distancemay, for example, be associated with a particular value of aninteraction force (e.g., the van der Walls force) between the tips. Arelatively referenced measurement is made of the known tip-to-tipdistance (e.g., a measurement made with respect to X_(L)Y_(L)Z_(L)). Theknown tip-to-tip distance can then be used to establish a relationshipbetween the X_(L)Y_(L)Z_(L) coordinates of a region of the left probetip that is involved in the tip-to-tip interaction and theX_(R)Y_(R)Z_(R) coordinates of the region of the right probe tip that isinvolved in the tip-to-tip interaction. A calibration using a knowntip-to-tip distance for which the tips have a known interaction can beused to remove the effect of probe shape from relatively referencedmeasurement data so as to recover dimensions of a feature (e.g., itswidth).

A caliper AFM can be calibrated by positioning the tips such that theirextreme lateral points are at a known tip-to-tip distance for which theyhave an known interaction; and measuring a measured interaction of theextreme lateral points of the tips. This type of calibration can occurfor a situation in which the tips are coordinated so as to make thetip-to-tip distance between the extreme lateral points zero. This can beaccomplished, for example, by operating the tips with respect to eachother in contact mode, as illustrated in FIG. 26. Alternatively, thetip-to-tip distance between the extreme lateral points may be a knownnon-zero value.

A caliper AFM can be calibrated by characterizing each apex with theother apex. This can be accomplished, for example, by fixing the lefttip with respect to XYZ and making a relatively referenced measurementby scanning the right tip over the left tip, as illustrated in FIG. 27.A contact mode scan can be used to scan each apex with the other apex.Alternatively, a non-contact mode scan can be used if a there is a knowntip-to-tip distance, for example, the fly height associated with aparticular value of an interaction force (e.g., the van der Waals force)between the tips. Alternatively, the left tip can be used tocharacterize the right tip, as illustrated in FIG. 28. In lieu of fixingeither tip with respect to XYZ, both tips can be scanned with respect toeach other to generate a relatively referenced data set. Once obtained,the relatively referenced data set resulting from characterizing eachtip with the other tip apex can then be used to establish a relationshipbetween the X_(L)Y_(L)Z_(L) coordinates of the region of the left probetip that is involved in the tip-to-tip interaction and theX_(R)Y_(R)Z_(R) coordinates of the region of the right probe tip that isinvolved in the tip-to-tip interaction. This relationship can be used toremove the effect of probe shape from relatively referenced measurementdata so as to recover dimensions of a feature (e.g., its width).

In-Line Calibration of a Caliper AFM

Calibration of a caliper AFM can be performed repeatedly before, duringand after measurements are made with the caliper AFM. Calibrationmethods, such as a tip-to-tip calibration method, that do not requireuse of an artifact, are available with a caliper AFM and areparticularly useful when there is a need to perform in-line calibrationduring a production process. For example, the presence of tip wear maycause excessive error buildup while a sequence of feature measurementsare being made to control production. Calibration steps performedbetween measurements can reveal the presence of such error build up.Also, the size of the required calibration adjustments can be monitoredand this observed trend can be used to increase (or decrease) thefrequency of calibration. Alternatively, repeated calibrations with anartifact can be made between measurements.

Traceable Calibration of a Caliper AFM

Traceable calibration of a caliper AFM can be accomplished by (1) makinga measurement for which the result is known in a way that can be tracedto an absolute dimensional standard, such as, for example, a wavelengthof light, or a number of crystal lattice intervals and (2) adjusting thescale of the caliper AFM so that its reading corresponds to the known,traceable dimension.

Traceable Measurement Using a Caliper AFM

One way to arrive at a traceable measurement of feature size is to firsttraceably calibrate the caliper AFM, and then generate two data setsassociated with the left and right AFM probes as relative coordinates ofeach tip with respect to the other. In making these measurements, thepositioning of each probe must be traceable. This can be accomplished byusing a sensor to ascertain the probe positions that is, itself,calibrated over the required range in a traceable manner. In this case,both data sets contain the same information. The extent of the featureis provided directly by the data set. Another way is to make a traceablemeasurement is to first traceably calibrate the caliper AFM, thengenerate two data sets as absolute coordinates of each tip with respectto the tool frame, and finally take the difference between recordedvalues so as to derive the extent of the feature. In making thesemeasurements, the positioning of each probe must be traceable. Thissecond way generates both the image of the feature (i.e., its shape withrespect to a tool-fixed frame) and its extent.

Roughness Measurement

The points included in a line roughness (LR) measurement on an arbitrarypath along which the measurement is taken contain information about theroughness of the feature on the path, as illustrated in FIGS. 29-31. Thepath along the edge of the feature is defined by the projection of thefeature onto a horizontal plane, as illustrated in FIG. 32. Itrepresents the edge of the feature as it would appear in a top-downimage.

A three dimensional linewidth roughness (3DLWR) measurement is made bymaking multiple line roughness (LR) measurements. Multiple linewidthroughness (LWR) measurements are determined from corresponding pairs ofLR measurements made at different heights, Z, as illustrated in FIG. 33.The multiple LWR measurements, taken together, comprise the threedimensional linewidth roughness.

Fourier transformation of LR data can be used to derive a line roughnessspectrum S, which can be expressed in terms of spatial period, asillustrated in FIG. 34. Typically, sharpness of the probe tip and thedynamic range of the AFM control system limit the ability to measureline roughness spectrum at small spatial periods. The overall length ofthe path used to generate the LR data limits the ability to measure lineroughness spectrum at large spatial periods. A similar analysisperformed on LWR data instead of LR data can be used to derive alinewidth roughness spectrum (LWRS).

Scanned Stage Embodiment of Caliper AFM

In another embodiment of the dual-probe caliper AFM architecture, calledthe scanned-stage embodiment, the dual probes are fixed with respect tothe tool frame and the stage carrying the feature is scanned in X and Z.The positions and orientations of the probes are adjustable prior toscanning. Adjustment can also occur during scanning, for example, toclear a feature bottom while the other probe is scanning it.

The feature first encounters the left probe at the top of the feature,as illustrated in FIG. 35-A. The left probe scans along the top of thefeature as the stage is translated in X and then along its left side, asthe stage is raised in Z. The left probe eventually reaches the trenchat the left side of the feature. The stage is then traversed in X untilthe right probe first encounters the feature at the trench on its sideof the feature, as illustrated in FIG. 35-B. The right probe then scansalong the right side of the feature, as the stage is lowered in Z. Thetilt of the probes enables them to access vertical and reentrantsidewalls. The feedback controller allows handoff between scanning ofthe left and right tips.

The scanned-stage embodiment, by the nature of its operation, removesthe contribution of the probe width from of the line width measurement.The stage travel (X_(AR)−X_(AL)) is first measured as the distancebetween stage positions at which the left and right sides of a referenceartifact encounter the left and right probes, respectively. Thereference artifact is assumed to have a known width, W_(A). The stagetravel (X_(AR)−X_(AL)) in the case of the reference artifact measurementis given by(X _(AR) −X _(AL))=(X _(R) −pw _(R) −sf _(R) −W _(A))−(X _(L) +pw _(L)+sf _(L))(X _(AR) −X _(AL))=(X _(R) −X _(L))−(pw _(R) +pw _(L))−(sf _(R) +sf_(L))−W _(A)(X _(AR) −X _(AL))=(X _(R) −X _(L))−pw−(sf _(R) +sf _(L))−W _(A)  (2)

A feature is then scanned using the dual probe AFM. The width, W_(F), ofthe feature is given by:W _(F)=(X _(R) −pw _(R) −sf′ _(R))−(X _(FR) −X _(FL))−(X _(L) +pw _(L)+sf′ _(L))W _(F)=(X _(R) −X _(L))−pw−(sf′ _(R) +sf′ _(L))−(X _(FR) −X _(FL))  (3)where pw is effectively the probe width and sf′_(R) and sf′_(L)represent tip-surface distance contributions that may possibly vary fromscan to scan, e.g., if non-contact scanning mode is used.

The terms (X_(R)−X_(L))−pw are eliminated by substituting the stagetraverse measurement, Equation (2) made using the reference artifact.This givesW _(F)=(X _(AR) −X _(AL))+(sf _(R) +sf _(L))+W _(A)−(sf′ _(R) +sf′_(L))−(X _(FR) −X _(FL))W _(F)=(X _(AR) −X _(AL))+[(sf _(R) +sf _(L))−(sf′ _(R) +sf′ _(L))]−(X_(FR) −X _(FL))+W _(A)  (4)

This procedure entirely eliminates the effective probewidthpw=(pw_(R)+pw_(L)) of the dual tip AFM. It leaves only the residualdifference in respective tip-surface offset distances,[(sf_(R)+sf_(L))−(sf′_(R)+sf′_(L))], instead of the involving fullmagnitude tip-surface offset in the measurement, as in the case of theconventional single-tip technique.

The effective probe width of the scanned-stage embodiment is essentiallyabsorbed into the left-right stage traverse determined while measuring areference artifact. This embodiment therefore relies on the dimensionalstability of the reference artifact for the integrity of criticaldimension measurements, instead of relying on the characterized shape ofa single-probe tip use with a conventional AFM, which may possibly wearor become damaged during use.

The scanned-stage embodiment is useful for measuring both isolated andnested features. In general, nested features may have different widths;different sidewall shapes and even different pitch (feature-to-featurespacing), as illustrated in FIG. 36. Nested features can be scannedusing a method that repeats the steps for scanning an isolated line. Theleft probe first encounters a point on the rightmost feature. The stagescans in X and Z so as to image the feature top and left sidewall. Thescan controller then executes handoff to the right probe, and scans theright sidewall. The stage is then moved in X so as to clear the firstfeature and bring the left probe into contact with the second feature.The scanning process then repeats for subsequent features.

Unlike imaging of isolated lines, imaging of dense lines is quiteintolerant of changes in tilt angle. For given feature geometries andgiven pitch there will be a constrained set of probe tilts which willallow both probes to access the trenches and the sidewalls of densefeatures. If the tilt angle is too small, the probe will not be able toaccess the sidewalls of reentrant features. Excessive tip tilt willcrash the tip into adjacent features. The required tip tilt depends onthe feature width and pitch of the features, on their aspect ratio, andthe sharpness of the tip. Introducing a system with three tilts enablesthe required dual-tilted-probe positioning. Rotating each probe aroundits long axis [“Tilt 1”] enables access to the feature sidewalls.Clearance with respect to the sample is required to avoid crashing ofthe probe's edges into the sample. The width of the probe and itsmounting structure, together with tip length, control the degree of Tilt1. Lowering of the oscillator tip down with respect to its base [“Tilt2”] provides clearance for the probe mounting structure. Pivoting eachprobe around its tip axis [“Tilt 3”] and pivoting their mountingstructures away from each other, together with beveling of the ends ofthe probe structure allows for side-to-side proximity without crashingthe edges of the probes with respect to each other.

Multiple-Head Embodiment of Caliper AFM

Another embodiment of the dual-probe caliper AFM architecture, calledthe multiple-head embodiment, uses multiple scanned-head caliper AFMs,as illustrated in FIGS. 37-A and 37-B. This embodiment has the advantageof achieving high throughput and increased sampling speed by enablingmultiple measurement sites to be scanned simultaneously. Multiple headscan be made modular and re-positionable to accommodate arbitrarilyplaced measurement sites and different production process controlrequirements, which may call for sampling different numbers of sites.Having multiple heads available provides the flexibility to specifymore, or fewer, measurement sites per wafer as process statisticschange.

Quate et. al. have demonstrated feasibility of an array of AFM probesfor imaging and scanning probe lithography. Unfortunately, this conceptdoes not work for critical dimension measurements. This is because theprobes do not have any lateral force sensitivity, and because they areunable to access vertical and reentrant sidewalls. The multiple-headembodiment of the present invention multiplexes dual-probe caliper AFMswith respect to entire measurement sites, rather than attempting tomultiplex individual probes within a multiprobe array. This makes all ofthe advantages of the caliper AFM available at each site.

Using the scanned-head embodiment of the caliper AFM rather than thescanned-stage embodiment enables the tips of different caliper AFM headsto move in either the same direction or in opposing directions asnecessary to accommodate simultaneous scanning of features at differentlocations.

A need for compactness stems from the requirement to fit multiplecaliper AFM heads within a confined region adjacent to the sample. Forexample, 5 to 10 caliper AFM heads may be required to fit within thefootprint of a single wafer. This requirement for compactness imposes alimitation on the size of the caliper AFM head. For example each caliperAFM head may be no more than about 2 inches on a side. A side viewillustrates a caliper AFM head designed to achieve the requiredcompactness.

MEMS Embodiment of Caliper AFM

An alternative embodiment implements the caliper AFM using amicroelectromechanical system (MEMS) design. For this embodiment, thetwo probes (the oscillator and the tips) together with the sensing andactuating systems are integrated and significantly reduced in size. Inaddition, the macro stages that are used to rotate the two probes withrespect to each other are not needed with a MEMS caliper AFM. Theintegration, scaling, and the removal of macro stages make this MEMScaliper AFM less complex and less expensive to produce in massquantities and more robust and reliable and more suitable for massproduction. One application of the MEMS caliper AFM design is forcritical dimension (CD) measurements.

The architecture of the MEMS caliper AFM of this embodiment includes twoAFM oscillators microfabricated next to each other on a same chip withfew microns of clearance to allow the oscillators to move with respectto each other in XYZ. The oscillators can be designed to be parallel toeach other or to be pointed towards each other's end.

An integrated sensing and actuation system is used in another embodimentof the MEMS caliper AFM design, as illustrated in FIG. 38. One possiblesensor and actuator design is an electrostatic sensor and an actuator.In one example, a comb drive type (an array of parallel platecapacitors, 3800, 3801, 3802) sensor and actuator can be utilized. Inthis design a movable arm comb structure engages the fixed combstructure on each side of the fixed structure. The arm structure isattached to the substrate via flexible links that allow three degrees offreedom XYZ displacement. The caliper oscillators extend from the armstructure. The comb actuator is capable of vibrating the two oscillatorsat their resonant frequencies (multi resonances for each oscillator) andmoving the arm in XYZ directions via electrostatic actuation. A separatecomb structure or simpler plate capacitor may be implemented as areadout sensor for the vibration of the oscillators and the DCdisplacement of the oscillators during scanning. Alternatively, thesample may be scanned with a combination of a macro stage that carriesthe sample.

The above described electrostatic actuator and sensor system may beutilized in any other applications where sensing and actuating in 3-Dare required. With some minimal electronic control logic the pitch andtilt degrees of freedom may also be achieved with the same electrostaticactuator and sensor system.

A suitable flex link for the arm structure is an L-bracket connected tothe substrate at one end and connected to the arm structure on the otherend. The fabrication process will produce a single piece of structurethat includes the substrate, the flex link, the arm, the oscillator, andthe tips. The L-bracket allows displacement in XYZ by flexing in thegiven direction.

To function as a caliper, the tips of the MEMS caliper AFM may be ableto touch each other's apexes. There are several designs that may achievethis function. These tip designs are also applicable as a single tip AFMand as a macro AFM. In one preference each MEMS oscillator has avertical tip from which end a horizontal tip is fabricated asillustrated in FIGS. 39-42. In one tip design, the vertical tip can be acylindrical tip, or sharp conical or sharp pyramidal tip, and thehorizontal tip can be a horizontally protruding nanotube. Preferably,the nanotube is a carbon nanotube. Preferably, the horizontal carbonnanotube tip is grown directly on the vertical tip. In this tip design,the horizontal tips need to be long enough to touch each other beforethe edges of the two oscillators collide with each other. For thisreason, it is desired that the vertical tip be fabricated as close aspossible to the side of the oscillator proximate to the otheroscillator. To minimize the horizontal tip-to-tip distance it is desiredthat the inner sides of the tips (one looking towards the other tip) bevertical whereas the outer side of the tips can have any shape asrequired by the process.

A further alternative tip is one where the inner side is tilted so thatthe apexes are the closest points between the two tips and the roots ofthe top (opposite of the apex) are further apart, as illustrated in FIG.43. With this tilted tip design there is not necessarily a need forhorizontal tips since the tilted tip includes the vertical and thehorizontal attributes of the tip.

Alternatively, the tip can be fabricated in the shape of an arrow (amushroom or an umbrella) so as to have a sharp apex and a rim edge thatextends radially beyond the stem of the tip, as illustrated in FIG. 44.This design is different than the “boot-shaped” or “flared” tip of aprevious art design because the disclosed design includes a sharpconical apex. With this design, the two tips will touch each other withtheir rim edges. This design is specially suited for imaging of deepvias and holes and other radially symmetrical features. A previous art“boot-shaped” or “flared” tip would also work with the disclosed MEMScaliper AFM. The extreme lateral points of the tips can easily bedetected by first bringing them in lateral proximity and then scanningup and down until the maximum tip distance is detected. The maximum tipdistance indicates that the extreme lateral points of the tips areagainst each other.

Alternatively, the horizontal tip can be a silicon tip fabricated at theend of a vertical tip, as illustrated in FIGS. 45 and 46. Due to the 2-Dnature of the MEMS processing, the horizontal tip is preferably flat (inthe same plane as the oscillator) and with a sharp apex. The advantageof this design is that the sharp apex can be fabricated by masking andpatterning. In the prior art the sharpness of the vertical tips isachieved with the help of etching a vertical structure to a sharp point.

This horizontal tip design removes the need for the oscillators to betilted with respect to each other in three axes in order the touch eachother's extreme lateral points. The required clearances between theoscillators can be integrated into the fabrication process. Since thereis no need for tilting mechanisms, the entire MEMS caliper AFM design isfree of macro or micro mechanical stages, making it less complex andmore reliable.

One disadvantage of the existing AFM probes is that the tips are locatedright under the micron-sized oscillator and there is no way of observingtheir navigation and sample imaging from a top-down vision system. Thedesign of the caliper AFM has horizontally protruding tips that allowthem to be suitable for inserting a vision apparatus that will help withthe viewing of the sample under test and for navigation of the tips withrespect to the sample. Suitable vision systems are optical systems andscanning electron microscopes. The integrated sensing system allows ahigh numerical aperture lens to be positioned right above the tips. Theintegrated sensing system also allows an electronic lens with mm-sizedclearance above the sample to be utilized.

Any standard MEMS fabrication process is suitable for fabrication of thesensor/actuator system, the oscillators, and the tips. Some processescan also be done with the help of ion milling. The shape and the layoutof the sensor and actuator comb structures and the oscillators can bedone with the help of selective patterning and etching of silicon. Thearm structures need to be etched underneath to allow them to move freelyin space. Effectively, the arm structures are cantilevered structures.The flexible links described above will keep the arm attached to thesubstrate.

Actuation and sensing in the X direction can be achieved, for example,with electrostatic plates that are parallel in the Y direction.Actuation and sensing in the Y direction are achieved, for example, withelectrostatic plates that are parallel in the X direction. Out-of-planeactuation and sensing is can be achieved, for example, withelectrostatic plates that are parallel in the Z direction. The sensorand actuator structures need to be made of conductive material and needto be connected to electrodes to function as an electrostatic device. Atleast, the electrodes for the electrostatic sensor and actuator need tobe deposited on each arm and on each side of the fixed structure,doubled for each direction of freedom, in-plane and out-of-plane. Thesix sets of electrodes need to be electrically insulated from each otherso that a particular powering of an electrode set may produce thedesired displacement or sensing. A combination of doped conductivesilicon and deposited metal can be used to construct the electricallayout of the actuator and the sensor. Standard metal depositionprocesses used commonly in MEMS processing are applicable foraccomplishing these tasks.

The fabrication process needs to take into account that the oscillatorsare thin structures compared to the actuator and sensing structures.Therefore additional patterning, doping, and etching may be required toproduce two silicon structures with much different thickness. As anillustration, the thickness (the height) of the comb structures is 20microns and the thickness of the oscillator is 2 microns. On the otherhand, the width of both the comb structure and the oscillator are in thesame range, about 20 microns. The silicon substrate under the oscillatorand the tip has to be completely removed so as to enable access of thetips to a test structure underneath.

Fabrication of the tips adds additional process steps. The verticalsilicon tips have comparable height with the vertical comb structures,lay in the same plane and may be processed together. The horizontalsilicon tips, the horizontal comb structures, and the oscillator lay inthe same plane and may be processed together. Fabrication of the carbonnanotube tips requires yet another process that includes at least thesteps of, preparation of the substrate and growth of the carbon nanotubetips. In one fabrication method the two oscillators and the two tips maybe fabricated as separate units. In another fabrication method theoscillators and the tips may be fabricated together as one unit and thanseparated into two branches (effectively cutting the oscillator and thetip in two) by subsequent etching or ion milling. The fabrication of thetilted tips may be done by over-etching the vertical tips or by ionmilling them. The fabrication of the arrow tips may be accomplished byetching the vertical tips in two etch steps where one produces thevertical tips and the other produces the stem. The stem and the arrowmay also be need to be made of conductive material and need to beconnected to electrodes to function as an electrostatic device. Atleast, the electrodes for the electrostatic sensor and actuator need tobe deposited on each arm and on each side of the fixed structure,doubled for each direction of freedom, in-plane and out-of-plane. Thesix sets of electrodes need to be electrically insulated from each otherso that a particular powering of an electrode set may produce thedesired displacement or sensing. A combination of doped conductivesilicon and deposited metal can be used to construct the electricallayout of the actuator and the sensor. Standard metal depositionprocesses used commonly in MEMS processing are applicable foraccomplishing these tasks.

The fabrication process needs to take into account that the oscillatorsare thin structures compared to the actuator and sensing structures.Therefore additional patterning, doping, and etching may be required toproduce two silicon structures with much different thickness. As anillustration, the thickness (the height) of the comb structures is 20microns and the thickness of the oscillator is 2 microns. On the otherhand, the width of both the comb structure and the oscillator are in thesame range, about 20 microns. The silicon substrate under the oscillatorand the tip has to be completely removed so as to enable access of thetips to a test structure underneath.

Fabrication of the tips adds additional process steps. The verticalsilicon tips have comparable height with the vertical comb structures,lay in the same plane and may be processed together. The horizontalsilicon tips, the horizontal comb structures, and the oscillator lay inthe same plane and may be processed together. Fabrication of the carbonnanotube tips requires yet another process that includes at least thesteps of, preparation of the substrate and growth of the carbon nanotubetips. In one fabrication method the two oscillators and the two tips maybe fabricated as separate units. In another fabrication method theoscillators and the tips may be fabricated together as one unit and thanseparated into two branches (effectively cutting the oscillator and thetip in two) by subsequent etching or ion milling. The fabrication of thetilted tips may be done by over-etching the vertical tips or by ionmilling them. The fabrication of the arrow tips may be accomplished byetching the vertical tips in two etch steps where one produces thevertical tips and the other produces the stem. The stem and the arrowmay also be fabricated by etching the vertical tip with two differentetching rates, where while the stem is etched away, the arrow isprotected from etching and vice versa. Clearly, MEMS embodiments includea very great variety of features.

Any element in a claim that does not explicitly state “means for”performing a specified function, or “step for” performing a specificfunction, is not to be interpreted as a “means” or “step” clause asspecified in 35 U.S.C. § 112, ¶ 6. In particular, the use of “step of”in the claims herein is not intended to invoke the provision of 35U.S.C. § 112, ¶ 6.

It should be apparent from the foregoing that an invention havingsignificant advantages has been provided. While the invention is shownin only a few of its forms, it is not just limited to those forms but issusceptible to various changes and modifications without departing fromthe spirit thereof.

1. A method of calibrating a caliper AFM having a first tip of a firstAFM probe and a second tip of a second AFM probe, the method comprising:positioning the first tip in proximity of the second tip, wherein, theproximity is within a range of a surface force interaction; determininga reference position of the first tip with respect to the second tip;and adjusting the caliper AFM based on the reference position.
 2. Themethod of claim 1, wherein the positioning is by means of a contact modeof AFM operation, a noncontact mode of AFM operation, or an intermittentcontact mode of AFM operation.
 3. The method of claim 1, wherein thereference position of the first tip with respect to the second tip isdetermined using lateral extreme points of the first and second tips. 4.The method of claim 1, wherein the reference position of the first tipwith respect to the second tip is determined using multiple points inthe vicinity of the lateral extreme points of the first and second tips.5. The method of claim 1, wherein the reference position of the firsttip with respect to the second tip is determined using a first point onthe first probe and a second point on the second probe.
 6. The method ofclaim 1, further comprising: controlling the operation of the method sothat the required frequency of calibration is determined in response tothe results of past operations of the method.
 7. The method of claim 1,further comprising in-line calibration.